Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons

Abstract

This article presents some results of a geometric classification of Sasakian manifolds (SM) that admit an almost ∗-Ricci soliton (RS) structure (g,ω,X). First, we show that a complete SM equipped with an almost ∗-RS with ω≠ const is a unit sphere. Then we prove that if an SM has an almost ∗-RS structure, whose potential vector is a Jacobi vector field on the integral curves of the characteristic vector field, then the manifold is a null or positive SM. Finally, we characterize those SM represented as almost ∗-RS, which are ∗-RS, ∗-Einstein or ∗-Ricci flat.